∫(3x+1)/(x^2+2x+17 )dx

来源：百度知道编辑：UC知道时间：2024/06/14 18:44:20

太难了......T_T 请写出具体步骤,谢谢

解：
∫(3x+1)/(x^2+2x+17)dx

=3∫x/(x^2+2x+7)dx +∫1/(x^2+2x+17) dx

=3∫1/2*(2x+2-2) /(x^2+2x+17) dx+∫1/(x^2+2x+17)dx

=3/2*∫(2x+2)/(x^2+2x+17) dx -3∫1/(x^2+2x+17)dx +∫1/(x^2+2x+17) dx

=3/2 *∫1/(x^2+2x+17) d(x^2+2x+17) -2∫1/((x+1)^2+16) dx

=3/2*ln|x^2+2x+17| -2*1/4arctan(x+1)/4 +C

=3/2*ln|x^2+2x+17| -1/2*arctan((x+1)/4)+C

高数，5555

确实很难喔！！~~

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